What will I have to pay? In 2014, the penalty will be no more than $285 per family or 1% of income, whichever is greater. In 2015, the cap rises to $975 or 2% of income. And by 2016, the penalty will go to $2,085 per family or 2.5% of income, whichever is greater.

The dollar amounts for a single adult would be $95, $325 and then $625 during that same time period. The dollar amounts per child would be half that of adults.

The penalty will be pro-rated based on the number of months during the year that you're uninsured, although those who are uninsured for less than three months in a given year would not be subject to the penalty.

The Congressional Budget Office estimates that roughly 4 million people a year will opt to pay the penalty instead of getting coverage. (Related: What's next for your insurance)

Does everyone have to pony up if they aren't insured? No. Some individuals will be exempt.

For instance, the penalty will be waived for people with very low incomes who don't have to file tax returns, those who are members of certain religious groups, or people who face insurance premiums that would exceed 8% of family income even after including employer contributions and federal subsidies.

For other examples of who is exempt, here's a helpful flow chart from Kaiser.

How will anyone know if I'm insured? Your insurance provider will have to send you and the IRS a form confirming that you have the minimum essential coverage. When you file your 1040, you will attach that form to your return.

Think of it like a 1099 form on which your bank reports your interest income to you and the IRS, Shulman noted in a presentation at the National Press Club.

If you don't have insurance, you will be assessed a penalty payment that you must send when you file your return.

What happens if I don't pay the penalty? The IRS will send you a letter stating that you owe the government money.

"These are not the kinds of things ... that we send agents out about. These are things where you get a letter from us," Shulman said.

"In the case of any failure by a taxpayer to timely pay any penalty imposed by this section, such taxpayer shall not be subject to any criminal prosecution or penalty with respect to such failure," according to the law.

The law also prohibits the government from putting liens or levies on your property to collect the penalty.

But based on Shulman's comments, it seems the government will be able to withhold your future refunds.

"We can actually do collection, if need be," he said. "People can get offsets of their tax returns in future years, so there's a variety of ways for us to focus on things like fraud, things like abuse."

What's not clear is whether failure to pay the penalty for not having insurance would subject you to late payment penalties to the IRS, much the same way a failure to pay your taxes on time would.